Percentage

[silverflamein]

45% of students in a school are girls. Among the students who have traveled abroad earlier, 25% are girls and among the one's who have not, 25% are boys. if the difference between the number of students who have traveled abroad and the number of those who have not is 105,what is the total number of students in that school ??

A)852
B)754
C)620
D)525
E)458

[shankar.ashwin]

Without doing any algebra here, you know Boys and Girls are 55% and 45% of total respectively.

Only option C gives you a whole number for the percentages. Boys and girls cannot be in decimals. So I would pick 620 without doing any math here.

[shankar.ashwin]

But are you sure the answer choices are right?

If 620 is the total, and the diff between people who have traveled and not traveled is 105

We have people who travelled abroad = (x+105)
People who have not = x

Adding, we have 2x+105=620
But x will not be an integer here. SO I think the option are not right here.

[rijul007]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

[silverflamein]

Well the options could be wrong. But they are the options that are given for the question

[rijul007]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

oooops
this is what we get if you solve using algebra...
but this solution is not possible because the no of girls or no of boys cant be in fractions [lol]
So the options provided seem to be wrong

[Guzcon]

If we call the number of students going abroad is X, then the number of girls going abroad is 25%X = 1/4X
If we call the number of students not going abroad is Y, then the number of girl not going abroad is 75%Y = 3/4Y

So the total numbers of girls in school is A = 1/4X + 3/4Y

X = 105 + Y

=> A = 1/4 (105+Y) + 3/4Y
=> A = 105/4 + Y

105/4 is not an integer, while A and Y must be integers.

I'm stuck here, could any one help me? Am I wrong somewhere?

[neelgandham]

I think the difference between the number of students who have traveled abroad and the number of those who have not is not-105. Nevertheless, If this is the question posed in the GMAT exam, where I get no one to complain to, I would go with 620.

why ?

(45/100) * Students = Girls

=> 9/20 * Students = Girls

=> # of Students should be a multiple of 20, and only 620 satisfies the condition !

[rohit_gmat]

assuming this Q was correct...

i got D when i did it with algebra.. but i took 6 min !!!!!!!!!

is that too long? anyone else facin the same prob? need ur inputs

[sl750]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

This calculation looks suspect. You have failed to account for the boys in your calculation

[sl750]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

This calculation looks suspect. You have failed to account for the boys in your calculation

[rijul007]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

This calculation looks suspect. You have failed to account for the boys in your calculation

the ques. says,
Among the students(x) who have traveled abroad earlier, 25% are girls and among the one's who have not(y), 25% are boys[rest 75% are girls].

Hence the total no of girls is 25% of x + 75% of y => x/4 + 3y/4

[sl750]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

This calculation looks suspect. You have failed to account for the boys in your calculation

the ques. says,
Among the students(x) who have traveled abroad earlier, 25% are girls and among the one's who have not(y), 25% are boys[rest 75% are girls].

Hence the total no of girls is 25% of x + 75% of y => x/4 + 3y/4

My contention is not in that particular step you took. A part of the question says, "if the difference between the number of students who have traveled abroad and the number of those who have not is 105"

The x component includes both boys and girls who have gone abroad
The y component includes both boys and girls who have not gone abroad

[rijul007]

No of students who have gone to abroad = x
No of students who have not gone to abroad = y

25% of x = no of girls who have gone abroad
75% of y = no of girls who havent gone abroad
Total no of girls = 45% of (x+y)

Hence,
x/4 + 3y/4 = 45(x+y)/100
on solving this eq we get
x = 3y/2


Acc to the ques,
x-y = 105
=>3y/2 - y = 105 [x = 3y/2]
y = 210
x=3(210)/2 = 315

Total no of students = x+y = 210 + 315 = 525


The correct option is D

This calculation looks suspect. You have failed to account for the boys in your calculation

the ques. says,
Among the students(x) who have traveled abroad earlier, 25% are girls and among the one's who have not(y), 25% are boys[rest 75% are girls].

Hence the total no of girls is 25% of x + 75% of y => x/4 + 3y/4

My contention is not in that particular step you took. A part of the question says, "if the difference between the number of students who have traveled abroad and the number of those who have not is 105"

The x component includes both boys and girls who have gone abroad
The y component includes both boys and girls who have not gone abroad

yes, both x and y include boys as well as girls...
and that's why i have taken teh equation
x-y=105